Machine presses of the type indicated in the foregoing are known and in use in diverse versions and configurations. In particular, DE 102009052531 A1 and DE 102012013098 A1 belong to the pertinent prior art. Machine presses in which the hydraulic linear drive comprises at least one hermetically sealed hydraulic drive unit, as it does according to the two documents mentioned in the foregoing, are characterized by various practical advantages compared with such machine presses in which the hydraulic linear drive comprises at least one open hydraulic drive unit, i.e. a hydraulic drive unit with a tank that is vented to the atmosphere. In this respect it must be emphasized in particular that such machine presses are able to satisfy even those requirements that are imposed on clean-room technology. Incidentally, the fact that the at least one hydraulic drive unit of the hydraulic linear drive is hermetically sealed makes it possible to impress a particular base pressure on the hydraulic system, which in turn is advantageous in several respects. An appropriate initial pressure permits a reduction of the line cross sections with simultaneous enhancement of the dynamic response of the hydraulic drive unit, without resulting in the danger of cavitation. A machine press constructed with particularly compact hydraulic drive units can be inferred from DE 102012013098 A1 since, in the respective hydraulic drive unit, one and the same pressure accumulator on the one hand (directly) pressurizes the raising working chamber and on the other hand—via a pressure transformer—supplies an initial pressure in the hydraulic system.